It isn't a human bone. It's from a quadrupedal (four legged animal) but difficult to tell which as it is broken. Not really fossilised either I'm afraid (although I understand why you say that as animal bones can be very dense and heavy). It has clearly been in the water a very long time though as it has worn some of the features away.

not good at this .. bone but i found a hunk of bone nr richmond bridge thinking it was mammoth but was told by museum i was cow ... althoug hit as heavy and felt nealtly like stone .. So similar dark brown colour too